Melanie Phillips is "In search of the work ethic" in her new two-part BBC Radio 4 programme – or, more accurately, seeking out why elements of the working class seem not overburdened with guilt when they are not working. In fact, what she found in the first programme this week was a simple economic truth. People don't like to work (or work harder) for no more money. Hence the poverty trap – many on benefits would be much worse off in work because benefits are removed pound for pound in line with their new wage.

Not a remarkable discovery, then. What is more interesting is the growing pay gap between the high-paid and low-paid – which, in many cases, is caused by falling pay among the poor. An Office of National Statistics salary survey at the end of last year showed gross median shelf-fillers' wages falling by 4.8%, road sweepers' falling by 2.6% and waiters and waitresses' by 11.4%. Meanwhile, managers' and senior officials' pay rose by 1.7% generally; notably, the top pay in local government went up 18.6%. Administrators benefited, newspaper journalists lost out (minus 3%) – but broadcasters did well and, remarkably, those in artistic and literary occupations saw pay rising 9.6%. The picture is mixed but generally the comfortably-off do better than those near the breadline.

So the real issue is why we pay less and less to the less well paid, expecting them to work more and more, while we pay more and more to the best paid?

Here's the Nerdonomics answer: if your hourly wages are raised from £5 to £6, say neoclassical economists, you face two effects: the substitution effect and the income effect.

In the first case, a good angel on your shoulder, steeped in Phillips's work ethic, says: "You're being paid more per hour, so it's worth doing an extra couple of hours' work since that work will be better rewarded than under your old contract." That's the substitution effect based on the idea that the opportunity cost of leisure has increased by a pound per hour: you're losing £6 by not working, instead of £5, so you substitute into work.

But the little devil on your other shoulder says: "Yes, maybe, but you've always been happy enough with your old wage. Why not ease off the accelerator, cut your hours back to give yourself the same wage but with less work?" That's the income effect. You gain leisure and lose no money. You're feckless and idle and probably spend the extra couple of hours a week down the pub.

For those who believe that big salaries should just get bigger, the implication is that top people are driven largely by the first effect. The more money you give them, the more they want to work.

In contrast, the working classes have only little devils driving them. So dissolute and lazy are they that if you give them more money, they simply want to take more time off and go and spend it. Keep the wages low and they might keep working. This, indeed, is what Phillips found among Britain's poor migrant community – a work ethic based on fear of destitution.

Meanwhile, the economic theory would suggest that, if you cut the pay of the better-off, they would work less. But if the work ethic is really written into their DNA, surely that can't be true. We may actually be paying them too much – and possibly bringing closer the time when they can almost give up work altogether – just like the poor on benefits. We might be stuffing the goose with gold and stopping it laying the eggs.

So here's how to prove the existence of the work ethic. Pay the people we currently pay a lot ... a lot less than we currently pay them. Halve the salaries of the rich. What effects will then come into play?

First, they will be confused and hurt. Don't we want their valuable labour? Yes, we do – that's why we are paying them less for it: so they will keep doing more.

Then the little angel will get them on track, urging them on to redouble their efforts to get their income up to the old level. They'll start working harder. They will increase their hours, because that is the sort of people they are: focused, not feckless. Prudent, not profligate.

It could be a bold experiment – but a guinea pig is needed. Step forward Melanie Phillips. Her programme exhibited a kinder, gentler Mel. Perhaps she may want to give up being a top Daily Mail writer and BBC broadcaster and return to the world of ill-paid old-fashioned journalism? Half the pay for twice the work. Go on, Mel, you know you'd love it.

Is British society fair? And if it's not - is it time to get angry? We take a look at the pay gap as inflation leaves those at the bottom struggling. And the film industry takes on the financial crisis